TSTP Solution File: GRP149-1 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : GRP149-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:17:44 EDT 2022
% Result : Unsatisfiable 0.70s 1.03s
% Output : Refutation 0.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP149-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 23:27:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.70/1.03 ============================== Prover9 ===============================
% 0.70/1.03 Prover9 (32) version 2009-11A, November 2009.
% 0.70/1.03 Process 2816 was started by sandbox on n007.cluster.edu,
% 0.70/1.03 Mon Jun 13 23:27:25 2022
% 0.70/1.03 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_2662_n007.cluster.edu".
% 0.70/1.03 ============================== end of head ===========================
% 0.70/1.03
% 0.70/1.03 ============================== INPUT =================================
% 0.70/1.03
% 0.70/1.03 % Reading from file /tmp/Prover9_2662_n007.cluster.edu
% 0.70/1.03
% 0.70/1.03 set(prolog_style_variables).
% 0.70/1.03 set(auto2).
% 0.70/1.03 % set(auto2) -> set(auto).
% 0.70/1.03 % set(auto) -> set(auto_inference).
% 0.70/1.03 % set(auto) -> set(auto_setup).
% 0.70/1.03 % set(auto_setup) -> set(predicate_elim).
% 0.70/1.03 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.70/1.03 % set(auto) -> set(auto_limits).
% 0.70/1.03 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.70/1.03 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.70/1.03 % set(auto) -> set(auto_denials).
% 0.70/1.03 % set(auto) -> set(auto_process).
% 0.70/1.03 % set(auto2) -> assign(new_constants, 1).
% 0.70/1.03 % set(auto2) -> assign(fold_denial_max, 3).
% 0.70/1.03 % set(auto2) -> assign(max_weight, "200.000").
% 0.70/1.03 % set(auto2) -> assign(max_hours, 1).
% 0.70/1.03 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.70/1.03 % set(auto2) -> assign(max_seconds, 0).
% 0.70/1.03 % set(auto2) -> assign(max_minutes, 5).
% 0.70/1.03 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.70/1.03 % set(auto2) -> set(sort_initial_sos).
% 0.70/1.03 % set(auto2) -> assign(sos_limit, -1).
% 0.70/1.03 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.70/1.03 % set(auto2) -> assign(max_megs, 400).
% 0.70/1.03 % set(auto2) -> assign(stats, some).
% 0.70/1.03 % set(auto2) -> clear(echo_input).
% 0.70/1.03 % set(auto2) -> set(quiet).
% 0.70/1.03 % set(auto2) -> clear(print_initial_clauses).
% 0.70/1.03 % set(auto2) -> clear(print_given).
% 0.70/1.03 assign(lrs_ticks,-1).
% 0.70/1.03 assign(sos_limit,10000).
% 0.70/1.03 assign(order,kbo).
% 0.70/1.03 set(lex_order_vars).
% 0.70/1.03 clear(print_given).
% 0.70/1.03
% 0.70/1.03 % formulas(sos). % not echoed (18 formulas)
% 0.70/1.03
% 0.70/1.03 ============================== end of input ==========================
% 0.70/1.03
% 0.70/1.03 % From the command line: assign(max_seconds, 300).
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.70/1.03
% 0.70/1.03 % Formulas that are not ordinary clauses:
% 0.70/1.03
% 0.70/1.03 ============================== end of process non-clausal formulas ===
% 0.70/1.03
% 0.70/1.03 ============================== PROCESS INITIAL CLAUSES ===============
% 0.70/1.03
% 0.70/1.03 ============================== PREDICATE ELIMINATION =================
% 0.70/1.03
% 0.70/1.03 ============================== end predicate elimination =============
% 0.70/1.03
% 0.70/1.03 Auto_denials:
% 0.70/1.03 % copying label prove_ax_lub1d to answer in negative clause
% 0.70/1.03
% 0.70/1.03 Term ordering decisions:
% 0.70/1.03
% 0.70/1.03 % Assigning unary symbol inverse kb_weight 0 and highest precedence (9).
% 0.70/1.03 Function symbol KB weights: a=1. b=1. c=1. identity=1. multiply=1. greatest_lower_bound=1. least_upper_bound=1. inverse=0.
% 0.70/1.03
% 0.70/1.03 ============================== end of process initial clauses ========
% 0.70/1.03
% 0.70/1.03 ============================== CLAUSES FOR SEARCH ====================
% 0.70/1.03
% 0.70/1.03 ============================== end of clauses for search =============
% 0.70/1.03
% 0.70/1.03 ============================== SEARCH ================================
% 0.70/1.03
% 0.70/1.03 % Starting search at 0.01 seconds.
% 0.70/1.03
% 0.70/1.03 ============================== PROOF =================================
% 0.70/1.03 % SZS status Unsatisfiable
% 0.70/1.03 % SZS output start Refutation
% 0.70/1.03
% 0.70/1.03 % Proof 1 at 0.08 (+ 0.00) seconds: prove_ax_lub1d.
% 0.70/1.03 % Length of proof is 45.
% 0.70/1.03 % Level of proof is 10.
% 0.70/1.03 % Maximum clause weight is 13.000.
% 0.70/1.03 % Given clauses 75.
% 0.70/1.03
% 0.70/1.03 1 multiply(identity,A) = A # label(left_identity) # label(axiom). [assumption].
% 0.70/1.03 4 greatest_lower_bound(a,c) = a # label(ax_lub1d_1) # label(hypothesis). [assumption].
% 0.70/1.03 5 greatest_lower_bound(b,c) = b # label(ax_lub1d_2) # label(hypothesis). [assumption].
% 0.70/1.03 6 multiply(inverse(A),A) = identity # label(left_inverse) # label(axiom). [assumption].
% 0.70/1.03 7 greatest_lower_bound(A,B) = greatest_lower_bound(B,A) # label(symmetry_of_glb) # label(axiom). [assumption].
% 0.70/1.03 8 least_upper_bound(A,B) = least_upper_bound(B,A) # label(symmetry_of_lub) # label(axiom). [assumption].
% 0.70/1.03 9 least_upper_bound(A,greatest_lower_bound(A,B)) = A # label(lub_absorbtion) # label(axiom). [assumption].
% 0.70/1.03 11 multiply(multiply(A,B),C) = multiply(A,multiply(B,C)) # label(associativity) # label(axiom). [assumption].
% 0.70/1.03 14 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(least_upper_bound(A,B),C) # label(associativity_of_lub) # label(axiom). [assumption].
% 0.70/1.03 15 least_upper_bound(A,least_upper_bound(B,C)) = least_upper_bound(C,least_upper_bound(A,B)). [copy(14),rewrite([8(4)])].
% 0.70/1.03 16 multiply(A,least_upper_bound(B,C)) = least_upper_bound(multiply(A,B),multiply(A,C)) # label(monotony_lub1) # label(axiom). [assumption].
% 0.70/1.03 17 least_upper_bound(multiply(A,B),multiply(A,C)) = multiply(A,least_upper_bound(B,C)). [copy(16),flip(a)].
% 0.70/1.03 18 multiply(A,greatest_lower_bound(B,C)) = greatest_lower_bound(multiply(A,B),multiply(A,C)) # label(monotony_glb1) # label(axiom). [assumption].
% 0.70/1.03 19 greatest_lower_bound(multiply(A,B),multiply(A,C)) = multiply(A,greatest_lower_bound(B,C)). [copy(18),flip(a)].
% 0.70/1.03 20 multiply(least_upper_bound(A,B),C) = least_upper_bound(multiply(A,C),multiply(B,C)) # label(monotony_lub2) # label(axiom). [assumption].
% 0.70/1.03 21 least_upper_bound(multiply(A,B),multiply(C,B)) = multiply(least_upper_bound(A,C),B). [copy(20),flip(a)].
% 0.70/1.03 22 multiply(greatest_lower_bound(A,B),C) = greatest_lower_bound(multiply(A,C),multiply(B,C)) # label(monotony_glb2) # label(axiom). [assumption].
% 0.70/1.03 23 greatest_lower_bound(multiply(A,B),multiply(C,B)) = multiply(greatest_lower_bound(A,C),B). [copy(22),flip(a)].
% 0.70/1.03 24 least_upper_bound(least_upper_bound(a,b),c) != c # label(prove_ax_lub1d) # label(negated_conjecture) # answer(prove_ax_lub1d). [assumption].
% 0.70/1.03 25 least_upper_bound(a,least_upper_bound(b,c)) != c # answer(prove_ax_lub1d). [copy(24),rewrite([8(5),15(5),8(4),15(5,R),8(4)])].
% 0.70/1.03 26 multiply(inverse(A),multiply(A,B)) = B. [para(6(a,1),11(a,1,1)),rewrite([1(2)]),flip(a)].
% 0.70/1.03 31 least_upper_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),least_upper_bound(A,B)). [para(6(a,1),17(a,1,1))].
% 0.70/1.03 32 greatest_lower_bound(identity,multiply(inverse(A),B)) = multiply(inverse(A),greatest_lower_bound(A,B)). [para(6(a,1),19(a,1,1))].
% 0.70/1.03 34 least_upper_bound(identity,multiply(A,B)) = multiply(least_upper_bound(A,inverse(B)),B). [para(6(a,1),21(a,1,1)),rewrite([8(5)])].
% 0.70/1.03 42 multiply(inverse(inverse(A)),identity) = A. [para(6(a,1),26(a,1,2))].
% 0.70/1.03 48 multiply(inverse(inverse(A)),B) = multiply(A,B). [para(26(a,1),26(a,1,2))].
% 0.70/1.03 49 multiply(A,identity) = A. [back_rewrite(42),rewrite([48(4)])].
% 0.70/1.03 58 multiply(A,inverse(A)) = identity. [para(48(a,1),6(a,1))].
% 0.70/1.03 64 inverse(inverse(A)) = A. [para(48(a,1),49(a,1)),rewrite([49(2)]),flip(a)].
% 0.70/1.03 84 least_upper_bound(identity,multiply(inverse(A),greatest_lower_bound(A,B))) = identity. [para(9(a,1),31(a,2,2)),rewrite([6(7)])].
% 0.70/1.03 130 greatest_lower_bound(identity,multiply(inverse(a),c)) = identity. [para(4(a,1),32(a,2,2)),rewrite([6(10)])].
% 0.70/1.03 131 greatest_lower_bound(identity,multiply(inverse(b),c)) = identity. [para(5(a,1),32(a,2,2)),rewrite([6(10)])].
% 0.70/1.03 154 greatest_lower_bound(A,multiply(inverse(a),multiply(c,A))) = A. [para(130(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 0.70/1.03 157 greatest_lower_bound(A,multiply(inverse(b),multiply(c,A))) = A. [para(131(a,1),23(a,2,1)),rewrite([1(2),11(5),1(8)])].
% 0.70/1.03 276 greatest_lower_bound(inverse(a),inverse(c)) = inverse(c). [para(58(a,1),154(a,1,2,2)),rewrite([49(6),7(5)])].
% 0.70/1.03 280 least_upper_bound(identity,multiply(a,inverse(c))) = identity. [para(276(a,1),84(a,1,2,2)),rewrite([64(4)])].
% 0.70/1.03 298 multiply(least_upper_bound(a,c),inverse(c)) = identity. [para(280(a,1),34(a,1)),rewrite([64(5)]),flip(a)].
% 0.70/1.03 304 inverse(least_upper_bound(a,c)) = inverse(c). [para(298(a,1),26(a,1,2)),rewrite([49(6)])].
% 0.70/1.03 310 least_upper_bound(a,c) = c. [para(304(a,1),64(a,1,1)),rewrite([64(3)]),flip(a)].
% 0.70/1.03 353 greatest_lower_bound(inverse(b),inverse(c)) = inverse(c). [para(58(a,1),157(a,1,2,2)),rewrite([49(6),7(5)])].
% 0.70/1.03 395 least_upper_bound(identity,multiply(b,inverse(c))) = identity. [para(353(a,1),84(a,1,2,2)),rewrite([64(4)])].
% 0.70/1.03 402 multiply(least_upper_bound(b,c),inverse(c)) = identity. [para(395(a,1),34(a,1)),rewrite([64(5)]),flip(a)].
% 0.70/1.03 408 inverse(least_upper_bound(b,c)) = inverse(c). [para(402(a,1),26(a,1,2)),rewrite([49(6)])].
% 0.70/1.03 453 least_upper_bound(b,c) = c. [para(408(a,1),64(a,1,1)),rewrite([64(3)]),flip(a)].
% 0.70/1.03 454 $F # answer(prove_ax_lub1d). [back_rewrite(25),rewrite([453(4),310(3)]),xx(a)].
% 0.70/1.03
% 0.70/1.03 % SZS output end Refutation
% 0.70/1.03 ============================== end of proof ==========================
% 0.70/1.03
% 0.70/1.03 ============================== STATISTICS ============================
% 0.70/1.03
% 0.70/1.03 Given=75. Generated=1888. Kept=446. proofs=1.
% 0.70/1.03 Usable=66. Sos=316. Demods=288. Limbo=1, Disabled=81. Hints=0.
% 0.70/1.03 Megabytes=0.53.
% 0.70/1.03 User_CPU=0.08, System_CPU=0.00, Wall_clock=0.
% 0.70/1.03
% 0.70/1.03 ============================== end of statistics =====================
% 0.70/1.03
% 0.70/1.03 ============================== end of search =========================
% 0.70/1.03
% 0.70/1.03 THEOREM PROVED
% 0.70/1.03 % SZS status Unsatisfiable
% 0.70/1.03
% 0.70/1.03 Exiting with 1 proof.
% 0.70/1.03
% 0.70/1.03 Process 2816 exit (max_proofs) Mon Jun 13 23:27:25 2022
% 0.70/1.03 Prover9 interrupted
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